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3 years ago

Solve each system by substitution.

Mathematics

1 answer:

Assoli18 [71]3 years ago

3 0

This how you set the equation up.
2x + 6 = 3x + 7
Subtract 6 from both sides.
2x = 3x + 1
Subtract 3x from both sides.
-1x = 1
Divide.
x = -1.
Now solve for y by plugging in the variable.
y = 2(-1) + 6
y = -2 + 6
y = 4
So your solution is (-1,4).
I hope this helps love! :)

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Among all pairs of numbers with a sum of 238238, find the pair whose product is maximum. Write your answers as fractions reduced

mylen [45]

Answer:

$x=119119,\;\;\;y=119119$

Step-by-step explanation:

Let the $x$ be the first number, $y$ be the second number and $p$ be the product of the first and second number.

i.e $x+y=238238$ $\Rightarrow x=238238-y$

$p=xy$

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$\Rightarrow \frac{dp}{dy} =238238-2y\\\Rightarrow 0=238238-2y\\\Rightarrow 2y=238238\\\Rightarrow y=119119$

Now,

$x=238238-119119\\\\ \Rightarrow x=119119$

Hence, $x=119119,\;\;\;y=119119$

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2 years ago

Write an equation of the translated function of the parent function f(x)=|x| with the following transformations:

MrRa [10]

Answer:

Option b

Step-by-step explanation:

To write the searched equation we must modify the function f (x) = | x | in the following way:

1. Do y = f(x + 4)

This operation horizontally shifts the function f(x) = | x | by a factor of 4 units to the left on the x axis.

y = | x +4 |

2. Do $y = f (\frac{1}{4}x)$

This operation horizontally expands the function f (x) = | x | in a factor of 4 units. $y = |\frac{1}{4}x + 1|$

3. Do $y = f(x)-4$

This operation vertically shifts the function f (x) = | x | by a factor of 4 units down on the y-axis.

$y = |\frac{1}{4}x +1| -4$

4. After these transformations the function f(x) = | x | it looks like:

$f(x) = |\frac{1}{4}x +1| -4$

Therefore the correct option is option b. You can verify that your vertex is at point (-4, -4) by making f (-4)

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3 years ago

Which of the following is a solution of x2 + 4x + 25?

blondinia [14]

Solve for x:
x^2 + 4 x + 25 = 0 I ssume that's the notation.
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x^2 + 4 x = -25
Add 4 to both sides:
x^2 + 4 x + 4 = -21
Write the left hand side as a square:
(x + 2)^2 = -21
Take the square root of both sides:
x + 2 = i sqrt(21) or x + 2 = -i sqrt(21)
Subtract 2 from both sides:
x = i sqrt(21) - 2 or x + 2 = -i sqrt(21)
Subtract 2 from both sides:
Answer: x = i sqrt(21) - 2 or x = -i sqrt(21) - 2

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3 years ago

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Varvara68 [4.7K]

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